Some trapezoidal interval type-2 fuzzy Heronian mean operators and their application in multiple attribute group decision making

To date, type-2 fuzzy sets have attracted much more interest of the researchers, which are more capable to handle uncertain and imprecision information than type-1 fuzzy sets. Heronian mean is a classical mean aggregation operator which can effectively consider the interrelationships between various arguments. In this paper, we extend Heronian mean to trapezoidal interval type-2 fuzzy environment and present some aggregation operators, such as trapezoidal interval type-2 fuzzy generalized Heronian mean (TIT2FGHM) operator and trapezoidal interval type-2 fuzzy weighted generalized Heronian mean (TIT2FWGHM) operator. Then, we further discuss several desirable properties and particular cases when the parameters take diverse values in detail. Moreover, concerning multiple attribute group decision making problems in which the decision attributes are interdependent and the attribute values take the forms of interval type-2 fuzzy numbers, we propose a new approach based on TIT2FWGHM operator. Finally, we provide a numerical example of providers selection to illustrate the practicality and effectiveness of the proposed method and give a comparison analysis between the proposed method and existing methods.